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The Manchester Evening News says Henderson, 23, is 'frustrated' by his lack of playing time in the Premier League and has no intention of playing second fiddle to David de Gea again next season.
Tottenham, Chelsea and West Ham United have expressed interest in Henderson..
He is under contract at United until 2025 and is valued at around £40million.
Spurs could sell error-prone goalkeeper Hugo Lloris in the summer as his deal expires next year while Lukasz Fabianski, the incumbent number one at West Ham, is out of contract in four months.
Former Chelsea coach Frank Lampard encouraged an approach for Henderson last summer and his replacement Thomas Tuchel has already started both Kepa Arrizabalaga and Edouard Mendy in the league.
Henderson is believed to have expressed his dismay to United manager Ole Gunnar Solskjaer about a lack of opportunities in the Premier League.
The England international has started just twice in the league, the last of those coming at former club Sheffield United on December 17.
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